Definition:Scalar/Module
< Definition:Scalar(Redirected from Definition:Scalar (Module))
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This page is about Scalar in the context of Module Theory. For other uses, see Scalar.
Definition
Let $\struct {G, +_G, \circ}_R$ be a module, where:
- $\struct {G, +_G}$ is an abelian group
- $\struct {R, +_R, \times_R}$ is the scalar ring of $\struct {G, +_G, \circ}_R$.
The elements of the scalar ring $\struct {R, +_R, \times_R}$ are called scalars.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 26$. Vector Spaces and Modules
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Module